Spectral Hashing

Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)

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Authors

Yair Weiss, Antonio Torralba, Rob Fergus

Abstract

Semantic hashing seeks compact binary codes of datapoints so that the Hamming distance between codewords correlates with semantic similarity. Hinton et al. used a clever implementation of autoencoders to find such codes. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresh- olded eigenvectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigen- functions of manifolds, we show how to efficiently calculate the code of a novel datapoint. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes significantly outperform the state-of-the art.